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Carlos Pestana Barros & Nicolas Peypoch
A Comparative Analysis of Productivity Change in Italian and Portuguese Airports
WP 006/2007/DE _________________________________________________________
M. V. Ibrahimo and C. P. Barros
Capital Structure, Risk and Asymmetric Information:
Theory and Evidence
WP 05/2010/DE/UECE/CESA
_________________________________________________________
Department of Economics
WORKING PAPERS
ISSN Nº 0874-4548
School of Economics and Management TECHNICAL UNIVERSITY OF LISBON
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Capital Structure, Risk and Asymmetric Information: Theory and
Evidence
M. V. Ibrahimo and C. P. Barros 1
Abstract: This paper proposes a principal-agent model between banks and firms with risk and
asymmetric information. A mixed form of finance to firms is assumed. The capital structure of
firms is a relevant cause for the final aggregate level of investment in the economy. In the model
analyzed, there may be a separating equilibrium, which is not economically efficient, because
aggregate investments fall short of the first-best level. Based on European firm-level data, an
empirical model is presented which validates the result of the relevance of the capital structure of
firms. The relative magnitude of equity in the capital structure makes a real difference to the
profits obtained by firms in the economy.
Key-words: Risk, asymmetric information, credit and capital structure.
Jel Classification: D81, D82, G21 and G32
1. Introduction
Both in theoretical and empirical analyses, many scholars have been addressing thoughts to the
mix of capital structure which could explain a healthy functioning of companies in free market
economies.2 In the present climate of worldwide economic crisis, the interest in this issue has
again assumed a vital relevance.3
Following the groundbreaking article written by Modigliani and Miller (1958), the Modigliani-
Miller theorem formed the basis for modern thinking on capital structure. This basic theorem
states that, under a competitive, efficient market process, in the absence of taxes, bankruptcy
costs and asymmetric information, the value of a firm is unaltered by the manner in which it is
financed. In other words, it does not matter if the company capital is funded by issuing stock or
raising debt from financial institutions. In substance, this theorem proposes what is often called 1 Ibrahimo and Barros both teach at the Universidade Técnica de Lisboa, Instituto Superior de Economia e Gestão. 2 A good survey on capital structure is Rizov (2008). In relation to mix form of capital structure, see Hellmann and Stiglitz (2000). 3 On the recent economic crisis and the need for a sound capital structure, see for example Adrian and Shin (forthcoming), Koziol and Lawrenz (2009) Akerlof and Shiller (2009), Brunnermeier (2009), Caballero and Krishnamurthy (2009), Soros (2009), Zandi (2008), Shiller (2008), and Allen and Gale
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the capital structure irrelevance principle.
Subsequently, by considering corporate taxes in the former model, Modigliani and Miller (1963)
and Miller (1977) reached the conclusion that debt-leverage is an important way to increase the
net income of firms, due to fiscal savings. This is clear in their model of valuing a firm through
the notion of adjusted present value. While it is hard to agree on the exact extent to which the
results of Modigliani and Miller have shaped the capital markets, the argument used to support
the expansion of leverage does seem logical. With little doubt, their results can be used to justify
the near-limitlessness of financial leverage. Recently, in a different setting, under the context of
asymmetric information, Ibrahimo and Barros (2009b) have developed a study in which a
similar result is derived. In this paper, the animal spirit behavior of economic agents plays a
crucial role in determining the high level of debt in free market economies.
However, Gordon (1989), based on many studies, disputed the Modigliani-Miller capital
structure theory. For example, the pecking order theory, developed by Myers and Majluf
(1984), asserts that firms perform much better if capital structure is predominantly supported by
internal funds rather than by external funds. Thus, capital structure does matter for the adequate
performance of companies.
Recently, a number of empirical studies carried out in relation to the roles and the efficiency of
different forms of capital have not proved conclusive. Examples of these studies are: Margaritis
and Psillaki (2010) Yu and Aquino (2008), López-Iturriaga and Rodriguez-Sanz (2008), Kim,
Hesmati and Aoun (2006), Fattouh, Scaramozzino and Harris (2005), Tong and Green (2005),
and Hovakimian, Opler, and Titman (2002).
However, as concluded by Ibrahimo and Barros (2009b), we believe that companies have a real
incentive to become highly debt-leveraged, which explains the credit crunch and the consequent
present economic crisis.
Given the tendency of firms towards a high level of leverage, it is logical that the financiers call
for the need of firms to hold in their balance sheets a minimum level of own capital so as to be
financed for their investment projects. Theories of optimal financial structure can be derived,
with the optimal structure depending on the nature of the information problem being faced by
the principal and agents. However, this outcome would imply the elimination of the problem of
uncertainty faced by all participants in the financial market. Thus, the constraints imposed by
banks as to the critical level of own equity of firms makes sense.
In many theoretical papers, the optimal financial contracts between two parties assume either
the form of debt, as in de Meza and Webb (1987), Gale and Hellwig (1985), and Williamson
(1987), or the form of equity, as shown by de Meza and Webb in Stiglitz and Weiss (1981). As
(2007).
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mentioned above, empirical studies are not consistent with regard to the optimality of capital
structure.
By fixing a minimum level of the proportion of outside equity, we attempt to determine, in the
present study, the constrained-optimal level of capital structure and the nature of equilibrium in
the financial market under the context of asymmetric information. Moreover, as the empirical
findings remain inconsistent and debatable regarding the different impacts of debt and equity on
the performance of firms and accordingly on the aggregate level of investment, we test these
effects with data on 15 European markets over the period 1995-2007, compiled by Worldscope.
Assuming the framework of de Meza and Webb (1990) and Ibrahimo and Barros (2009a), the
structure of the model is defined in Section 2. The context is a simple one-period partial
equilibrium model of investment with informational asymmetries between risk-neutral banks,
which offer financial contracts, and risk-averse entrepreneurs, who demand funds for their
projects.
Section 3 develops the model with a mixed form of financial contracts. With this assumption
rather than debt finance alone, a non-efficient separating equilibrium is derived. In this
equilibrium, aggregate investment falls short of the first-best level. The resulting under-
investment (or under-lending) may be seen as a counter-intuitive outcome. However, it must be
noted that this is one side of a dual-market phenomenon, which affects the real economy, since
the other side of the duality must be the over-investment (or over-lending) effect in the use of
funds by financiers for pure speculation in financial products.
Another central result determined in this section is that the capital structure of firms does matter,
i.e. the relative magnitude of outside equity makes a real difference to the quantity of aggregate
investment and thus, to the level of aggregate profits in the real economy.
Section 4 proposes an empirical study testing the relevance of capital structure, with data on 15
European markets over the period 1995-2007, compiled by Worldscope. A random profit
frontier is estimated, which concludes that equity and debt have different impacts and roles in
the performance of companies. Finally, Section 5 offers a concise discussion of the pertinent
issues raised and also presents some concluding remarks.
2. A principal-agent model of finance
The economic environment is a simple one-period partial equilibrium model with
ex ante asymmetric information between banks and entrepreneurs. The analysis aims to
determine: (a) the nature of equilibrium; (b) the effects of the capital structure of firms;
(c) and the causes of market failures.
The basic assumptions of the model and the behavior of economic participants are
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defined below. Entrepreneurs' projects differ in terms of their level and nature of risk and the
problem analyzed is that of financing them by own equity, debt and outside equity. This
method of financing investors, which is common in the capital markets, is analogous to
that proposed in the study of de Meza and Webb (1990). The specific notion of risk is taken
from the model of Stiglitz and Weiss (1981).
Let us assume a capital market, in which there are only two classes of economic agents:
firms or entrepreneurs, who are in need of finance, and banks or financial institutions,
which make it available.
Entrepreneurs are risk-averse, expected utility-maximizers, all with an identical
quasi-concave utility function of end-of-period wealth, U (W). They each have the same
initial wealth, ,W0 which can be invested either in an indivisible amount of investment,
K, or in a safe asset, yielding the same interest rate ρ . For the sake of simplicity, it is
assumed that the deposit is the sole safe asset in the market, so that if projects are not
carried out, 0W is deposited with banks. The ith project, if executed, yields a random
return iR of siR if it succeeds and f
iR if it fails. Adaptation of the mean preserving
spread criterion of Rothschild and Stiglitz (1970) implies that all projects have a common
expected return µ :
(1) µ=−+ fi
sii
si
sii R)]R(p1[R)R(p , for all i.
In this equation, pi, defined by [0, 1], is the success probability of the ith project. To
simplify the model, we assume that ffi RR = for all i. Projects differ in risk and since pi
depends on siR , so they differ in successful return. In the present analysis, it is sufficient to
assume only two categories of entrepreneurs4: high-risk individuals with success probability
)R(p sHH and low-risk individuals with success probability )R(p)R(p s
HHsLL > . This
condition with (1) implies that projects are ranked by the mean preserving spread
criterion. In what follows the subscript i will denote the entrepreneur's category.
To cause the need for external finance, it is assumed that W0 < K, so if a project is to be
carried out, additional funds must be raised. This is done through the issuance of outside
equity and/or debt securities. Debt security of current value B pays in the successful state a
sum D = (1 + r)B, in which r is the borrowing loan rate, or else pays the entire project
return to the bank in the event of bankruptcy. Then, the return on debt is min (D, jR ) and
the return on equity is max 0) ,DR( j − , where j = s, f. The proportion of inside equity in the
4 The terms entrepreneur and project are used interchangeably.
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project is 10 ≤α≤ , which is held by the entrepreneur, and the remainder — the outside
equity — is sold to a bank. For the purchase of debt security, with face value of repayment
D, and the proportion (1 – α ) of the equity, the bank agrees to pay an amount F.
Successful states must pay off both entrepreneurs and banks. Therefore, it is reasonable to
assume DR si > . If a project of category i is successful, the entrepreneur’s end-of-period wealth
is:
(2) )KWF)(1()DR(W 0si
si −+ρ++−α= .
In the unsuccessful state, he obtains5:
(3) )KWF)(1()]0,DR[max( WW 0fff
i −+ρ++−α== .
From the expected utility theorem, the entrepreneur's preferences for income in the two
states of nature are described by the following function6:
(4) )W(U)p1()W(Up)W(EU fi
siii −+= , in which i = H, L.
The entrepreneur of category i will carry out his project if:
(5) ]W)1[(U)W(EU 0i ρ+≥ .
A small group of large banks is willing to offer funds. They are assumed to be
competitive, risk-neutral, expected profit-maximizers. Competition is of Bertrand type in price
strategies. Banks pay for each unit of deposits a safe interest rate ρ ; other costs of banks are
ignored. The supply of funds to a bank is assumed to be non-decreasing in the safe rate
of interest. It is assumed that banks have knowledge of the proportion of each of the
two categories of entrepreneurs, ]1,0[i ∈λ with 1HL =λ+λ . Moreover, they know the
success probability pi of each type. However, banks cannot distinguish ex ante the
characteristics of each entrepreneur's project. This assumption introduces the key asymmetry
of information into the model. Once finance is made available, the financial contract specifies
its terms F, α and D. With this contract offered to an entrepreneur of category i, in the
successful state the bank makes a profit of:
(6) F)1()DR)(1(D si
sBi ρ+−−α−+=π , i = H, L.
The bank’s profit in the low state is:
(7) F)1()0,DRmax()1()R,Dmin( fffB
fBi ρ+−−α−+=π=π .
The value of fR can be greater or smaller than D. Therefore, the expected profit to the 5 For a given contract, note that ff
iff
i RR since i, all for,WW == . 6 Utilities are assumed not to be state-dependent.
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bank from a project of category i resulting from the financial contract offered:
(8) fBi
sBiiBi )p1(p)(E π−+π=π .
Note that )R(pp siii = .
In the present model, collusion between banks is ruled out and each entrepreneur can
only carry out one project.
The following definition is now established:
Definition 1: Equilibrium in the competitive capital market is specified by a set of
financial contracts, such that all contracts in the equilibrium set generate a zero
expected profit to banks; and there exists no other contract in the exterior of the
equilibrium set, which - if offered - yields a non-negative expected profit.
Definition 1 means that there is a Bertrand competition between banks. In other words,
each bank expects that the rivals will maintain the terms of financial contracts invariable,
in spite of its own decisions.
Next, we develop the model under the constrained-mixed form of finance and the properties
of the market equilibrium are then examined.
3. Financial equilibrium in a model of the mixed form of finance
The theory of financial markets with asymmetric information, with few exceptions, treats debt
and equity as extreme, alternative means of finance. This is so because optimal
contracts are derived under very restrictive assumptions. On this matter, it seems that
the theory of the capital structure of modern corporations uses an approach more consistent
with the real world. For example, Jensen and Meckling (1976) argue that in entrepreneurial
firms where the resources of entrepreneurs are limited, projects are not in general
exclusively funded by means of just one source of finance. In this study, it is illustrated that an
optimal combination of debt and equity can be obtained if the effects of adverse
incentives - from issuing new equity - and risk distortions - from issuing debt - are
equalised at the margin. An analogous point of view is advanced by Williamson
(1988). Thus, it seems constructive to study the effects of a mixed form of finance of the capital
needed by firms for their entrepreneurial projects.
Accordingly, we presume a particular combination of debt and equity. In all financial contracts
offered, let α be fixed and greater than φ = [– fW + µ + (1 + ρ ) (W0 – K)] / ( µ – fR ),
i.e. α = α > ϕ . This constraint is not implausible and allows a clearer comparison with the
7
Stiglitz and Weiss (1981) model. As in this study, if α > ϕ , riskier projects yield a lower
expected profit for banks. In addition, let Dmax be the maximum amount of debt allowed for
both categories of entrepreneurs. The assumptions of the model indicate that if finance is made
available, D ≤ Dmax < sLR < s
HR . Let us also consider that 0 < fR < D. Now, for a given
contract (F*, α *, D*), equations (2) and (3) become:
(9 ) siW = α ( s
iR - D+ ( 1 + ρ ) (F+W 0 - K),
(10) fiW = fW = (1 + ρ ) (F+ W 0 - K)
Equations (6) and (7) become:
(11) sBiπ = D + (1 – α ) ( s
iR – D) – (1 + ρ ) F,
(12) fBiπ = f
Bπ = fR – (1 + ρ ) F.
In equilibrium, equation (8) must be equal to zero, for a separating equilibrium if i = H, L,
and for a pooling equilibrium if i = A. Using equations (9), (10), (11) and (12) in the
zero expected profit condition, the mathematical function for the offer curves is obtained in
(F, D) space:
(13) D = [ )1( ρ+ / pi α ] F+ siR – µ /pi α .
In this equation, the measure of slope is (1 + ρ )/piα, which is clearly steeper for the
riskier category of entrepreneurs. If p i = p A = λ L pL+ (1 – λ L) pH and siR = s
AR , equation
(13) describes the pooling offer curve.
Indifference curves of entrepreneurs are obtained by substituting equations (9) and (10) for siW
and fW into equation (4):
(14) p i U [ α ( SiR -D) + (1 + ρ ) (F +W0 –K)]+
+ (1 +pi) U [(1 + ρ ) (F+ W0 – K)] = u .
In this functional relationship, u is a constant and denotes a utility level. It can
easily be shown that these curves are concave and steeper, at any geometric point, for the
riskier projects. Furthermore, indifference curves of each category are steeper, at any
geometric contract-point, than the banks’ respective increasing offer line
Now, equilibrium in the model with asymmetric information is exposed. The next definition
is advanced.
Definition 2: Let Hv and Lv be contracts selected by the high- and low-risk entrepreneurs,
respectively. If they involve equilibrium and cannot be displaced by any other contract on offer,
then Hv and Lv are said to be dominant contracts.
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This definition requires an incentive-compatibility relationship between banks and
entrepreneurs. With LH vv = , equilibrium will be settled through a pooling contract, and with
LH vv ≠ through a pair of separating contracts.
Taking into account Definition 2 and with very restrictive assumptions, pooling equilibrium
may exist. Nevertheless, under plausible conditions, equilibrium, if it exists, must be settled
through a pair of separating contracts. These results are shown by Ibrahimo and Barros (2009a).
We now discuss the welfare properties of the equilibrium and the consequent policy
implications. Some models of the credit market show that - from a production point of view -
separating equilibrium involves the first-best solution (e.g. de Meza and Webb, 1990; Bester,
1985). However, diverging from this result, the following proposition is established.
Proposition 1: With plausible assumptions such that α = α > ϕ and µ=µi for all i, at
the competitive separating equilibrium, aggregate investment is below its respective socially
efficient level.
The proof of this is rather complex and is offered in the study of Ibrahimo (1993).
The particular case of the market considered here exhibits in equilibrium an efficiency
problem. As in the Rothschild and Stiglitz model, there is a negative externality of high-risk
categories on low-risk categories. The externality is purely dissipative. In other words, utilities
in social terms are wasted. Comparing with the solution of perfect information, low-risk
categories are worse off, but high-risk categories are no better off. It is worth mentioning that
this type of externality - which is due to the nature of asymmetric information - is the main
cause of inefficiency that arises in the quantity of aggregate investment. In reality, the presence
of high-risk entrepreneurs in the market induces low-risk entrepreneurs to demand lower
amounts of debt than they would if information were perfect. With a large number of
entrepreneurial categories (i.e. not just two categories), since for each category a lower debt
involves a lower value paid by banks in exchange for bonds, the categories of projects with the
highest success probabilities become unprofitable from the point of view of entrepreneurs and
hence are not carried out. Thus, in equilibrium the quantity of aggregate investment falls short
of the first-best level.
The under-investment result suggests that a policy aimed at improving efficiency should
encourage more investment which could be achieved by a subsidy on bank financing. It
does appear, however, that such a policy must be second-best, since it would not dispose of
negative externality on low-risk individuals.
The present section also demonstrates that real economic decisions are not independent of
the corporate financial structures. Against the conclusions resulting from the Modigliani-Miller
proposition, it has been shown that the capital structure of firms does matter. Clearly, the
9
relative value of outside equity in the capital structure of firms produces a real difference in
the level of aggregate investment in equilibrium.
4. An empirical study related to the model
In order to test the above model, this section uses the profit frontier model of (Berger, Hancock
and Humphey, 1993; Mester, 1997) to test the relationship between profits and capital structure,
using the data on 15 European markets over the period 1995-2007, compiled by Worldscope.
The stochastic frontier model is characterized by the utilization of a two-component error term.
A symmetric component captures the random variation of the frontier across firms, statistical
noise, measurement error, and random shocks external to firm control. The other component is
a one-sided variable capturing inefficiency relative to the frontier. The stochastic profit frontier
is written as:
(15) T1,2, t N,1,2, i ; ituitve).itX(itR …=…=
+β=
where Rit represents a scalar profit of company i in the t-th period; Xit is a vector of known
inputs and outputs; β is a vector of unknown parameters to be estimated; the error term vit is
assumed to be independent and identically distributed and represents the effect of random
shocks (noise). It is independent of uit, which represents technical inefficiencies and is assumed
to be positive and to follow a N(0, su2) distribution. The disturbance uit is reflected in a half-
normal independent distribution truncated at zero, signifying that the profit of each firm must
lie on or above its profit frontier, implying that deviations from the frontier are caused by
factors controlled by the firm’s management. The variance of uit is σu2 (π-2)/π.
The parameterization of the different elements to the total variation is given as:
σv2 = σ2 / (1+ λ2) and σu
2 = σ2 λ2 / (1+ λ2); where λ = σu / σv , which provides an
indication of the relative contribution of u and v to εi = ui – vi, since estimation of
equation 1 yields merely the residualε, rather than u, the latter must be calculated
indirectly (Greene, 2003). For panel data analysis, Battese and Coelli (1988) used the
expectation of uit conditioned on the realized value of εit = uit - vit, as an estimator of
uit. In other words, E[uit|εi] is the mean productive profit inefficiency for company i at
time t. However, the inefficiency can also be due to the companies’ heterogeneity,
which implies the use of a random effects model:
(16) ititit´'
i0it Suv+xβ+)w+α(=R
10
where the variables are in logs and wi is a time-invariant specific random term that captures
individual heterogeneity. ui is the time-varying inefficiency. The sign of the inefficiency term,
S depends on whether the frontier describes production or cost function. Any heterogeneity is
either absent or contained in the profit function absorbed in two parameters, first, the time
invariant wi, which is interpreted as ‘producer profit inefficiency due perhaps to omitted inputs
and second, in the inefficiency time-varying term u.
The model is estimated in the following form:
(17)
[ ][ ]
[ ]2wi
ii
2uititit
2vit
itititiit
α,0N~w
w+α=ασ,0N~U,U=u
σ,0N~v
uv+x'β+α=R
Concerning the stochastic specification of the inefficiency term u, the half-normal distribution
is assumed to be time-variant. For the likelihood function, we follow the approach proposed
by Greene (2005), where the conditional density is:
(18) )σitε(φ
σ1
)0(Φ
)σ/λitε(Φ=)itε(f
where Φ is the standard normal distribution and φ is the cumulative distribution function.
Conditioned on wi, the T observations for company i are independent.
The log likelihood is computed by simulation (Greene, 2005, equation 31).
The equation to be estimated is the following:
(18)
11
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ccii
ii
r i r kr
rkkrriirkiik
k
ssrrs
rj mmkkm
kjiij
i
krr
i kkkii
lk lrrlkli
lii
DRSC
pZpPpZpQpPpQ
pZpZpPpPpQpQ
TpZTpPTpQ
pzpPpQTTpR
µεκρ
ϖκ
φϕθ
λλλ
φϕβττα
lnlnln
/ln/ln/ln/ln/ln/ln
/ln/ln/ln/ln/ln/ln21
/ln/ln/ln
/ln)/ln(/ln21/ln
15
11
2
1
3
1
2
1
3
13
2
133333
3
1
2
133
2
1
3
1
2
133
3
133
3
1
2
13
3
1
3
133
3 2
333
32
1113
++++
++Ω+
+++
+++
+++++=
∑
∑ ∑∑ ∑∑∑
∑∑∑ ∑∑∑
∑∑ ∑
∑ ∑∑
=
= = = = ==
=== ===
== =
= ==
where:
ln R is the natural logarithm of operating profit. A constant term φ is added if the firm reports an
operating loss. φ is equal to the absolute minimum operating profit plus one, so that the natural
log is taken of a positive number;
T is a time trend;
lnQ is the natural logarithm of firm output (sales or revenues);
lnPk is the natural logarithm of ith variable input prices (P1-the prices of labor defined as the
wages divided by the number of equivalent employees), P2-price of capital-premises
(amortizations divided by fixed assets) and P3-price of other assets (total costs minus
wages/fixed assets).P3 is used to normalize the function and therefore disappears from Table 1;
lnZr is the natural logarithm of fixed netput quantities z1-equity: 1-D and z2-debit: D);
lnRSCi is the natural logarithm of interest expense on debt. It is a proxy for the risk structure of
capital of each firm;
Mi is a country dummy;
εi are identical and independently distributed random variables, which are independent of the µi,
which are non-negative random variables that are assumed to account for inefficiency;
α, τ, β, ψ, λ, θ, φ, κ, Ω, ϖ, ρ, and κ are the parameters to be estimated using maximum
likelihood methods.
We obtained firm balance-sheet and income statements annual data (n euros and in real prices)
from Worldscope from 1995-2007. We selected the European countries listed in Table 1. There
are 20085 observations and the countries used to control the dummy trap are Turkey and
12
Finland. We exclude firms whose capital decisions may reflect special factors: The financial
sector (SIC codes 6000-6999) and regulated enterprises (SIC codes 4000-4999).
Standard restrictions of linear homogeneity in input prices and symmetry of the second-order
parameters are imposed on the profit function. Whilst the profit function must be non-increasing
and convex with regard to the level of fixed input and non-decreasing and concave with regard
to prices of the variable inputs, these conditions are not imposed, but may be inspected to
determine whether the cost function is well-behaved at each point within a given data set.
Table 1 here
Table 1 presents the characteristics of the variables and Table 2 below presents the results. We
estimate the random stochastic profit frontier model in equation and report the estimated
parameters in Table 2. For comparison, we report also the parameters derived from a non-
random specification of the profit function. How do we interpret these results? We can
conclude that the random frontier model better describes the underlying profit structure of
European firms the non-random or homogenous frontier model. This result supports claims that
non-random frontier models fail to disentangle firm-level heterogeneity from inefficiency with
the implication that inefficiency will be biased. In our models, the estimated lambda from the
random frontier implies that 25.9% of firms are attributable to inefficiency, whereas the
comparative figure is 66.3% for the non-random frontier. This means that 40.4% of firms’ costs
can be explained by heterogeneity within the sample firms. Thus, failing to account for
heterogeneity in the specification of the profit function will seriously bias estimated efficiencies,
which has implications for the design of public policy since it is clear that one hat will not fit all.
Similar conclusions are reached by Greene (2004, 2005b). Further support for the specification
of the random frontier is drawn from a likelihood test of the goodness-of-fit between the two
models. Since the likelihood test has a higher chi-square distribution for the random frontier, we
conclude that the random model better fits the data than the non-random model (see Table 1).
Table 2 here
Generally speaking, the estimated parameters from the non-random and random profit frontiers
tend to have the same signs, although the magnitude of coefficients and their T-statistics can
vary. The models appear to be consistent with expectations: profit increases with output, one
input price, and netput. The estimated parameters on the time trend and its quadratic term
indicate that the cost of European firms is increasing at a diminishing rate over time. We
identify one random parameter, which are firm sales or receipts. This implies that the source of
13
heterogeneity between firms operating in Europe between 1995 and 2007 resides in their
income statement sheet structures, which may be an indication of specialization in production,
possibly relating to firm size. This result also signifies that European firms are relatively
homogenous on the other variables.
Relative to the debt and stock, we verify that both contribute to increased profits, validating the
Modigliani-Miller hypothesis, but the square term of stock is positive, signifying that it
increases profits in an increasing rate, while the square term of debt is negative, signifying that
it increases profit at a decreasing rate. Moreover, the coefficient of stock is higher than that for
debt, which is logical given the risk related to debt. Furthermore, the proportion of interest
expense on debt indicates the level of credit risk assumed by a firm. If the amount of interest
expenses is high, this may be an indication that a firm has expended too much based on credit.
This is evidence of skimping behavior which states that companies deliberately choose not to
expand, but produce excessively risky credit as a direct consequence of their decision. The
parameter estimates for the non-random frontier show a very large and significant coefficient
for RSC (-0.532). This suggests that riskier firms with larger proportions of risk credit have
lower profits, which is evidence of financial stress. Based on these findings, it would be
reasonable for bank regulators to take corrective action against excessive debt. Therefore, it can
be concluded that too much debt can be detrimental to enterprises’ profits.
5. Discussion and concluding remarks
This paper argues that, contrary to the traditional views, but nevertheless in accordance
with the standpoints of some researchers as to the relevance of the capital structure of
modern corporations, there may be a constrained-optimal combination of debt and equity
for the capital structure of firms. Thus, the present study has developed a principal-agent model
for the financial market, in which the financial contracts offered by financiers to entrepreneurs
assume a mixed form of debt and equity. If the proportion of inside equity is relatively
outsized, the equilibrium, if it exists, may be unique and entails an offering of
separating contracts to investment projects with different risk categories. A novel result is that
separating equilibrium generates too little aggregate investment. Therefore, a subsidy on
bank financing could be Pareto-improving. However, because of negative externalities due to
the presence of high-risk individuals, it seems that the best a policymaker could hope for
would be to achieve a second-best allocation of credit.
The under-lending result achieved could be seen as counter-intuitive. However, it must be noted
that this is the phenomenon which affects the real-economy. Under this circumstance, there is
generally an incentive to use the excess money in banks for the purpose of speculation, which
could explain the over-lending for the purchase of innovative financial products.
14
The empirical work shows that debt may impact negatively on companies’ profits and the
contribution of stock is higher than debt for higher profits, justifying parsimonious use of debt
in investment projects. The present financial crisis highlights the depressing role of high levels
of debt in the capital structure of companies, which in contexts of economic crisis may lead
firms to bankruptcy. Hence, the present study argues that whilst debt may leverage the stock of
companies, too much debt is detrimental.
The fundamental result of our study also corroborates the views of some alternative theories as
to the importance of the soundness of the capital structure of firms, namely the pecking order
theory, in which it is argued that, due to the adverse selection problems, firms should prefer
internal to external finance. However, when outside funds are needed, firms should prefer debt
to equity, due to the lower information costs associated with debt issues. Under this condition,
equity is not often issued. These ideas were refined into a key testable prediction by Shyam-
Sunder and Myers (1999). The financing of deficit should normally be matched dollar-for-dollar
by a change in the corporate debt. Debt financing does dominate equity financing in magnitude.
Net equity issues do not track the financing decisions of companies. The underlying view of this
theory is that financial stress and the consequent economic crisis are most likely the effects of
the financing decisions of companies. However, it must be noted that the evidence relative to
this theory is mixed, as argued by Frank and Goyal (2003).
The general conclusion of the pecking order theory is that debt initially leverages the company’s
capital, but afterwards may be detrimental for profits and may cause the bankruptcy of the firm.
Summing up, this proposition is necessarily an essential issue for further empirical research.
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Table 1: Descriptive Statistics (in natural logarithms)
Variable Description Minimum Maximum Mean Standard deviation
OP Natural logarithm of operating profit
-3.987 1.100 -1.417 0.916
T Time 1 36 17.45
10.37
T2 Time squared 1 1296
412
387.07
Q1 Logarithm of Sales 0.108 2.721 1.202 0.605 P1 Price of labor defined as
wages divided by the number of equivalent employees
0.0006 0.698 0.367 0.151
P2 Price of capital-premises defined as amortizations divided by fixed assets
0.0006 0.826 0.385 0.166
Z1 Logarithm of fixed netput quantities-equity
-0.013
0.876
0.430
0.167
Z2 Logarithm of fixed netput quantities - debt
0 1.837
0.774
1.026
RSC Logarithm of interest expense on debt.
0.609
0.812
0.707
0.025
Austria Dummy variable for the country 0 1 0.016 Belgium Dummy variable for the country 0 1 0.028 Denmark Dummy variable for the country 0 1 0.037 France Dummy variable for the country 0 1 0.154 Germany Dummy variable for the country 0 1 0.169 Greece Dummy variable for the country 0 1 0.058 Italy Dummy variable for the country 0 1 0.045 Ireland Dummy variable for the country 0 1 0.012 Netherlands Dummy variable for the country 0 1 0.040 Norway Dummy variable for the country 0 1 0.025 Portugal Dummy variable for the country 0 1 0.015 Spain Dummy variable for the country 0 1 0.031 Sweden Dummy variable for the country 0 1 0.065
17
Switzerland Dummy variable for the country 0 1 0.048 UK Dummy variable for the country 0 1 0.257
Table 2: Parameter estimates: Non-Random and Random Stochastic Frontiers Non-
random frontier
Random frontier
Non-random frontier
Random frontier
Variables Coefficients (t-ratio)
Coefficients (t-ratio)
Variables Coefficients (t-ratio)
Coefficients (t-ratio)
Constant 0.864 (-0.106)
-0.213* (-2.286)
Z1Z2 0.314 (1.446)
0.347 (2.927)
T -0.066** (-11.912)
-0.04* (-2.157)
RSC -1.232 (-2.873)
-0.532 (3.452)
Q1 0.0006** (7.372)
0.052** (3.218)
Austria 1.035 (2.294)
1.134 (7.427)
P1 1.546** (8.878)
0.832** (4.392)
Belgium 0.051 (1.687)
0.030 (1.316)
P2 1.028 (1.098)
0.935** (2.782)
Denmark 1.718 (4.334)
1.989 (5.107)
Z1 0.228 (2.030)
0.400** (4.388)
France 0.203 (4.102)
0.303 (6.932)
Z2 0.145 (1.808)
0.157** (3.782)
Germany 0.394 (3.446)
0.347 (2.927)
1/2T2 0.321* (3.145)
0.352* (3.531)
Greece 1.334 (2.109)
1.709 (4.957)
1/2Q12 -0.007** (-4.505)
-0.019** (-2.694)
Italy 0.005 (2.791)
0.001 (3.252)
1/2P12 0.061** (3.348)
0.018* (3.293)
Ireland 0.904 (2.462)
0.812 (2.646)
1/2P22 0.049** (8.315)
0.015** (3.732)
Netherlands 0.357 (0.752)
1.272 (2.855)
1/2Z12 0.373 (11.674)
0.527 (3.728)
Norway 1.035 (2.294)
1.134 (7.427)
1/2Z22 -0.231 (-4.218)
-0.127 (-3.178)
Portugal 0.051 (1.687)
0.030 (1.316)
Q1T 0.125 (2.183)
0.274 (3.921)
Spain 3.718 (4.334)
1.989 (5.107)
P1T -0.053 (-0.506)
-0.052 (-3.518)
Sweden 0.203 (4.102)
0.303 (6.932)
P2T -0.109 (-0.966)
-0.021 (-1.782)
Switzerland 0.394 (1.446)
0.347 (2.927)
Z1T 0.232 (2.191)
0.126 (3.278)
UK 1.334 (2.109)
1.709 (-4.957)
Z2T 0.136 (2.126)
0.218 (3.031)
Mean for random parameters
Q1P1 1.035 (2.294)
0.303 (6.932)
Q1 0.254 (3.867)
Q1P2 -1.152** (-4.819)
-0.031* (-2.568)
Scale parameters for Dists. Of Random Parameters
1.837 (8.228)
Q1Z1 -1.152** (-4.819)
-0.031* (-2.568)
Q1 0.112 (7.622)
Q1Z2 -2.095** (-10.394)
-0.984** (-3.218)
v
u
σσ
λ = 0.663** (3.919)
0.259** (5.118)
18
P1P2 6.829** (5.763)
0.523 (1.784) [ ] 2/122
uv σσσ += 0.263
(13.975) 0.124
(4.586) P1Z1 (0.188)
(0.188) (2.452) (2.452)
Log likelihood 29.915 32.108
P1Z2 -6.315** (-2.963)
-0.945 (-1.218)
Likelihood ratio test
6.179 9.218
P2Z1 0.357 (2.796)
0.164 (1.245)
Observations 16738 16738
P2Z2 2.26 (1.629)
0.735** (4.215)